Numerically integrating with weight factors

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Tyler on 17 Aug 2013
Hi, i am integrating a stiffness matrix over two euler angles, phi, theta.
if i integrate the stiffness matrix over both angles, and then divide by the area of a unit sphere, it is treated as if each particular direction is weighted equally, and for a transversely isotropic material, when integrated will produce an isotropic material.
I am interested in biasing the integral however with a separate probability distribution (which i have at the moment as a gaussian curve revolved around an axis, in meshgrid form).
How do i specify when integrating - that i want the particular numerical integration function (say quad) to while integrating at a particular point phi,theta - to go and grab the weight factor from my table?
Is there any way to do this?
any help would be greatly appreciated.

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